Despite the wide acceptance of the “big-leaf” upscaling strategy in evapotranspiration modeling (e.g., the Penman-Monteith model), its usefulness in simulating canopy photosynthesis may be limited by the underlying assumption of homogeneous response of carbon assimilation light-response kinetics through the canopy. While previous studies have shown that the separation of the canopy into sunlit and shaded parts (i.e., two-leaf model) is typically more effective than big-leaf models for upscaling photosynthesis from leaf to canopy, a systematic comparison between these two upscaling strategies among multiple ecosystems has not been presented. In this study, gross primary productivity was modeled using two-leaf and big-leaf upscaling approaches in the Boreal Ecosystem Productivity Simulator for shrublands, broadleaf, and conifer forest types. When given the same leaf-level photosynthetic parameters, the big-leaf approach significantly underestimated canopy-level GPP while the two-leaf approach more closely predicted both the magnitude and day-to-day variability in eddy covariance measurements. The underestimation by the big-leaf approach is mostly caused by its exclusion of the photosynthetic contributions of shaded leaves. Tests of the model sensitivity to a foliage clumping index revealed that the contribution of shaded leaves to the total simulated productivity can be as high as 70% for highly clumped stands and seldom decreases below ∼40% for less-clumped canopies. Our results indicate that accurate upscaling of photosynthesis across a broad array of ecosystems requires an accurate description of canopy structure in ecosystem models.
Traditionally, many ecosystem models have used a simple light-use efficiency [Monteith, 1972, 1973] approach to estimate photosynthetic carbon assimilation by plant canopies (gross primary production (GPP)). Since the advent of the process-based “Farquhar” formulation of leaf photosynthesis [Farquhar et al., 1980], many ecosystem models have adopted this leaf-level model as a basis to upscale to the canopy, with some approaches assuming common physiological parameters throughout the canopy while others partition the canopy into different layers with distinct light-response features. Consequently, canopy-level GPP estimation offers a choice of leaf-to-canopy upscaling methodologies, with the approach potentially affecting the outcome of GPP simulations [e.g., Wang and Leuning, 1998; Dai et al., 2004; Liu et al., 1997; Chen et al., 1999].
The simplest of these upscaling methodologies is the “big-leaf” approach, which assumes that canopy carbon fluxes have the same relative responses to the environment as any single unshaded leaf on a canopy top [Sellers et al., 1992; Dai et al., 2004]. The applicability of a big-leaf approach [e.g., Kull and Jarvis, 1995; Friend et al., 1997] is justified by the assumptions that within canopies, photosynthetic capacity, primarily reflected in leaf nitrogen content, is distributed in proportion to the profile of radiation [de Pury and Farquhar, 1997].
Despite its wide acceptance for modeling evapotranspiration at different spatial scales [Raupach and Finnigan, 1988; Moran et al., 1996; Samson and Lemeur, 2001; Weiß and Menzel, 2008], subsequent theoretical and experimental developments [de Pury and Farquhar, 1997; Carswell et al., 2000; Lai et al., 2000; Meir et al., 2002] have brought into question assumptions behind the big-leaf approach in modeling vegetation productivity. It is well accepted in recent literature [e.g., Friend, 2001] that under realistic conditions, photosynthesis of most leaves is usually not light saturated and that, because of complex canopy architecture, the distribution of absorbed irradiance is highly variable and does not necessarily follow Beer's law for one-dimensional (1-D) canopy radiative transfer as assumed for the single leaf. These findings challenge the assumption that photosynthetic capacity is solely proportional to absorbed irradiance. Additionally, since total canopy nitrogen may greatly exceed that of a single leaf upscaled using the big-leaf approach, total photosynthesis of a canopy (which is correlated to total canopy nitrogen) may be higher than that derived from a single upscaled leaf [Kull, 2002], leading to an inadequate simulation of CO2 assimilation at the canopy level and to a consequent underestimation of GPP by big-leaf models.
While the most advanced radiative transfer algorithms developed for fine-scale (e.g., site-level) applications have improved on big-leaf models by relying on a computationally intensive radiative transfer code, there is a need for an intermediate approach that can be generalized for regional to global ecosystem modeling, where computational efficiency is paramount. A simpler sunlit-shaded leaf separation approach, within which the vegetation is treated as two big leaves under different illumination conditions, was proposed more than three decades ago [Sinclair et al., 1976] and has been continuously investigated since then [de Pury and Farquhar, 1997; Wang and Leuning, 1998; Chen et al., 1999; Mercado et al., 2006]. Two-leaf models have been successfully tested for applications at local and regional scales and have been found to sufficiently capture much of the variation present in complex multilayered sunlit-shaded leaf separation approaches [e.g., Kotchenova et al., 2004] in a way that the big-leaf upscaling cannot achieve [de Pury and Farquhar, 1997; Chen et al., 1999; Dai et al., 2004; Mercado et al., 2006, 2007].
Although the underestimation of GPP by the big-leaf approach could be improved by site-level tuning of photosynthetic parameters [e.g., Lloyd et al., 1995], such computationally intensive parameterization loses global-scale applicability. Thus, we focus here on the performance of big-leaf and two-leaf models when using the same leaf-level parameterization for several land-cover types across large latitudinal ranges. Direct comparisons of the two upscaling approaches at multiple sites have not been done to our knowledge. Given the still relatively common use of the big-leaf models (and its simplified formulation of light-use efficiency models) and the plethora of data now available for evaluation from the global network of flux towers, it is prudent to reevaluate how well two-leaf and big-leaf approaches simulate GPP and how the differences between both are sensitive to site land cover and location.
There are ecophysiological reasons to suspect that big-leaf models are likely to poorly simulate canopy GPP. First, photosynthesis of C3 plants is largely limited by the drawdown in CO2 concentrations from the atmosphere to the sites of carboxylation. Two steps dominate the pathway of CO2. The first is diffusion of CO2 from the atmosphere to substomatal cavities via the stomata. The second is its diffusion from the substomatal cavities to the sites of carboxylation via leaf mesophyll. The conductance inside the leaf mesophyll (also known as internal conductance) has been traditionally assumed infinite and therefore nonlimiting for photosynthesis. Recent evidence, however, points to mesophyll conductance that can be finite and highly variable [Flexas et al., 2008; Warren, 2008], suggesting that the diffusion from substomatal cavities to sites of carboxylation is at least as large a limitation of photosynthesis as stomata [Warren, 2008]. As formulated, the big-leaf approach scales only stomatal conductance [Sellers et al., 1992] while leaf internal regulation remains unchanged no matter how many layers of leaves are operating simultaneously (i.e., internal conductances are in parallel in reality). Such a way of scaling may lead to misinterpretation of the physiological mechanism of CO2 assimilation because one (i.e., big) leaf has only one mesophyll conductance. In reality, several layers of leaves operate simultaneous in assimilating CO2 from the atmosphere, meaning that several internal leaf conductances operate in parallel. As the mesophyll conductance to CO2 transfer is different in shaded and in sunlit leaves [Piel et al., 2002], a two-leaf approach avoids these drawbacks, accounting for the role of shaded leaves in the canopy-level photosynthesis, which averts the amplification of leaf internal control of the CO2 flow (i.e., too-small overall internal conductance) as imposed by the big-leaf model.
Second, the two-leaf representation is able to apply the separation of incoming radiation into its direct and diffuse portions. Sunlit leaf irradiance and shaded leaf irradiance are important variables because the penetrations of direct and diffuse radiation into the canopy vary [Weiss and Norman, 1985] and because they may have different effects on stomatal conductance and electron transport rate [Chen et al., 1999]. Therefore, as was stated by Norman [1980, p. 65]: “the failure to differentiate between diffuse beam and direct radiation within the canopy can lead to erroneous calculations of photosynthesis.”
Although in the two-leaf approach, the shaded leaf receives only diffuse light (while the sunlit one receives both direct and diffuse radiation [Spitters, 1986]), the diffuse portion is used much more efficiently for photosynthesis than direct radiation. Dai et al. [2004, Figure 5] show, for example, that the shaded part of the canopy can absorb most of the diffuse component of the incoming photosynthetically active radiation (PAR), actually leading to the increase of assimilation in changing from a very clear to overcast sky. Mercado et al. [2006, Figure 5] demonstrated that the big-leaf approach is unresponsive to variation in diffuse irradiance, which likely leads to an underestimation of the total canopy photosynthesis. Thus, the assumption that a canopy can be represented as a single unshaded leaf on a canopy top makes the big-leaf approach insensitive to processes such as sunfleck penetration and diffuse radiation in the canopy. In this case, if canopy absorption of diffuse radiation for GPP is significant, a big-leaf model will underestimate the diurnal and day-to-day variations in canopy photosynthesis. While diurnal variability between the two models is worthwhile to investigate, the significant variation in radiation during the day will generally blur the differences between big-leaf and two-leaf models. Consequently, a worthwhile test of the appropriateness of the big-leaf approach would be to compare how well two-leaf and big-leaf models represent daily variations in GPP, even if GPP magnitude is poorly simulated, since the latter effect can be reduced with site-specific parameter tuning. Saying that, it should be kept in mind that this lack of day-to-day variability in GPP simulated by the big-leaf model is caused not only by its inability to reflect the radiation control on shaded leaf photosynthesis, as analyzed above, but also by the amplified leaf internal resistance to the CO2 flow imbedded in the big-leaf formulation, which also makes the model insensitive to driving factors affecting the canopy photosynthesis.
Currently, there is a lack of systematic comparisons between two-leaf and big-leaf models at multiple field sites, leaving doubts on the suitability of either approach in the context of regional to global model simulations of GPP for multiple ecosystem types. Previous studies have shown the big-leaf approach to match [Sinclair et al., 1976; Mercado et al., 2006; Houborg et al., 2009;Alton et al., 2007], overestimate [de Pury and Farquhar, 1997; Dai et al., 2004], or underestimate [Chen et al., 1999; Friend, 2001; Mercado et al., 2007] eddy covariance (EC) measurements. Our study is the first to systematically investigate big-leaf and two-leaf upscaling strategies for canopy photosynthesis estimation using a well-tested ecosystem model across 11 flux tower sites in North American boreal and temperate regions. Our hypotheses are (1) big-leaf upscaling will underestimate canopy-level GPP compared with the two-leaf upscaling, and this underestimation is strongest in dense forest canopies with large fractions of shaded leaves, and (2) variance in daily GPP explained by the big-leaf approach will be less than that explained by the two-leaf approach when canopies absorb a significant quantity of diffuse radiation. On the basis of the investigation of these hypotheses against carbon flux data, we explain the likely physiological mechanisms that may lead to big-leaf or two-leaf mismatches against observations.
2.1. Study Sites
We selected 11 North American forested eddy covariance flux tower sites that are part of the Ameriflux and Canadian Carbon Program networks and used in the North American Carbon Program (NACP; http://www.nacarbon.org/nacp/) site-model intercomparison interim synthesis. The sites span North America from northern boreal latitudes (lat = 68°) to midlatitudes (lat = 35°). These sites are six broadleaf deciduous forests: the Old Aspen site (CA-Oas; Prince Albert National Park, Saskatchewan, Canada), the University of Michigan Biological Station (U.S.-UMB; Michigan), Sylvania Wilderness Area (U.S.-Syv; Michigan), Missouri Ozark Site (U.S.- MOz; University of Missouri's Baskett Wildlife Research and Education Area, Missouri), the Walker Branch watershed (U.S.-WBW; National Environmental Research Park, Oak Ridge, Tennessee) and the Tonzi ranch (U.S.-Ton; California); three evergreen coniferous forests: the Old Black Spruce forest (CA-Obs; Prince Albert National Park, Saskatchewan, Canada), the main tower of Howland Forest (U.S.-Ho1; Maine), and the Niwot Ridge temperate forest (U.S.-NR1; Roosevelt National Forest in the Rocky Mountains, Colorado); and two sites that could be classified as shrublands: Ivotuk (U.S.-Ivo, Alaska) and Mer Bleue (CA-Mer; Mer Bleue Eastern Peatland, Ontario, Canada).
Strictly speaking, the oak woodland savanna Tonzi ranch is not per se a broadleaf site [Chen et al., 2008]; however, since the overstory vegetation is 40% dominated by blue oak (Quercus douglasii), many regional to global ecosystem models classify the site as broadleaf deciduous forest, and, for consistency, we do the same. The same argument could be made for the Mer Bleue peat bog, which is a wetland site that we classify under the shrubland category while aggregating the detailed land-cover types (i.e., GLC2000; see section 2.6) to six plant functional types. Detailed descriptions of these sites are summarized in Table 1.
IGBP, International Geosphere-Biosphere Programme; DBF, deciduous broadleaf forest; ENF, evergreen needle-leaf forest; SHR, open shrubland; P, precipitation; Tair, air temperature; LAI, leaf area index; CA-Oas, Old Aspen site (California), U.S.-UMB, the University of Michigan Biological Station (Michigan), U.S.-Syv, Sylvania Wilderness Area (Michigan), U.S.-MOz, Missouri Ozark Site (Missouri), U.S.-WBW, the Walker Branch watershed (Tennessee), CA-Obs, Old Black Spruce forest (Canada); U.S.-Ho1, Howland Forest (Maine), U.S.-NR1, Niwot Ridge forest (Colorado). Clumping index after the work by Chen et al. .
The observed values of net ecosystem exchange (NEE) were corrected for storage and filtered to remove conditions of low turbulence. The gaps in the observations at all sites were filled using a consistent algorithm based on moving-window regression of NEE to environmental parameters [Barr et al., 2004]. Consistency in gap filling and NEE decomposition into GPP maintains fidelity of comparison across sites [Desai et al., 2008]. Additionally, estimates of uncertainty due to random processes and uncertainty due to the friction velocity filtering were also computed for each site [Barr et al., 2004; Schwalm et al., 2010]. GPP at each tower site was inferred from an established, common algorithm that first estimates ecosystem respiration (ER) by moving-window regression of nighttime NEE to temperature and establishes GPP as the difference between modeled ER and NEE. In this analysis, GPP was aggregated to daily integrals to reduce the impact of random errors.
2.2. Ecosystem Modeling
Simulations of GPP for both two-leaf and big-leaf models were made using the Boreal Ecosystem Productivity Simulator (BEPS) [Liu et al., 1997, 1999, 2002; Chen et al., 1999; Ju et al., 2006]. BEPS is driven by gridded meteorological (incoming shortwave radiation, air temperature, specific humidity, precipitation, and wind speed) and soil water holding capacity [Liu et al., 2002] data sets, and SPOT4 remotely sensed vegetation parameters (land-cover type and leaf area index(LAI)). Although the model was initially developed for boreal ecosystems and intensively tested over the Canadian landmass, it has been successfully implemented in temperate and tropical environments as well by adjusting the inputs to local environmental and biophysical conditions [e.g., Wang et al., 2004; Zhou et al., 2007; Feng et al., 2007].
The model calculates hourly carbon fixation by scaling Farquhar's leaf biochemical model [Farquhar et al., 1980] up to the canopy level following Chen et al. . With spatially explicit input data on vegetation, meteorology, and soil, BEPS can be run either pixel by pixel over a defined domain or can simulate canopy photosynthesis at a particular geographic location. Stomatal conductance is calculated by a modified version of the Ball-Woodrow-Berry model [Ball et al., 1987]. Incoming radiation is separated into diffuse and direct components following the semiempirical approach given by Erbs et al. , Black et al. , and Chen et al. . The mean energy budgets of sunlit and shaded leaves are calculated using the methods of Chen et al. . Since the emphasis of our study is on the differences between big-leaf and two-leaf approaches in simulating measured GPP for the purpose of demonstrating the issues with leaf internal resistance in the big-leaf formulation, we focus on the model's ability in capturing day-to-day GPP variability in this study. Therefore, the hourly modeled results are aggregated to daily values in order to clearly demonstrate the difference in model's response to day-to-day meteorological variations (particularly radiation) (Figure 2). Key equations of the model are described in Appendix A.
2.3. Two-Leaf Approach
BEPS was originally a two-leaf model that calculated GPP separately for sunlit (LAIsun) and shaded (LAIsh) parts of overstory and understory layers following the leaf stratification strategy [Norman, 1982]. The total canopy photosynthesis (A) is then estimated as the sum of representative sunlit (Asun) and shaded leaf (Ash) photosynthesis rates:
Both rates of photosynthesis are calculated using Farquhar's leaf biochemical model [Farquhar et al., 1980] combined with a physical model describing the CO2 flow from inside the stomatal cavity to the free air [Leuning, 1997]. We used separate leaf-level biochemical parameters for each canopy stratum, thereby acknowledging physiological differences in maximum carboxylation and electron transport rates that may have consequences for GPP (see Appendix A for equations).
The total leaf area index (LAI) is separated into sunlit and shaded LAI using the original formulation of Norman  with consideration of a foliage clumping index proposed by Chen et al. :
where θ is the solar zenith angle and G(θ) is the foliage projection coefficient taken as 0.5 assuming a spherical leaf angle distribution. Ω characterizes the leaf spatial distribution pattern in terms of the degree of its deviation from the random case (being unity for randomly distributed leaves and less than one for clumped canopies) and influences radiation interception by the canopy at a given θ as described by Beer's law.
2.4. Big-Leaf Approach
In Farquhar's model, the leaf-level photosynthetic capacity is described as the sum of all the chloroplast capacities in a given unit area, and the chloroplast properties are assumed to scale with the internal light gradient of the leaf [Farquhar and von Caemmerer, 1982]. A similar argument has been applied to plant canopies assuming an optimal distribution of leaf nitrogen through the canopy, which occurs when nitrogen is distributed in proportion to the distribution of the solar irradiance absorbed by the canopy, averaged over the time that leaves are able to acclimate (i.e., several days to a week). This implies that the vertical profile of photosynthetic capacity covaries more or less linearly with leaf nitrogen content [e.g., Ingestad and Lund, 1986]. Consequently, if the distribution of photosynthetic capacity among leaves in a canopy is proportional to the profile of absorbed irradiance (described by Beer's law), then the canopy can be treated as a homogeneous entity (i.e., big leaf), and the equations usually applied to single leaves might be used for the entire canopy [de Pury and Farquhar, 1997; Farquhar, 1989]. Stomatal conductance (g) upscaled to the canopy level by means of the total LAI (i.e., gLAI), electron transport rate is calculated from absorbed canopy-level PAR and net photosynthesis in an unshaded leaf (A0), which is consequently scaled to the total canopy value as proposed by Sellers et al.  and described in detail in numerous publications [e.g., Friend, 2001; Arora, 2003; Mercado et al., 2006, 2007; Alton et al., 2007]:
where the multiplicative factor (fscale) is equal to (1-exp(-k*LAI))/k and k is the canopy PAR extinction coefficient.
2.5. Clumping Simulations
Foliage clumping increases the probability of leaf overlapping and, as a result, decreases the probability of a leaf exposure to the direct radiation. A decrease in Ω (increasing clumping) results in a decrease of LAIsun and a consequent increase in the fraction of the shaded leaves. Since shaded leaves typically have higher light-use efficiency (photosynthetic performance per unit incident photon flux density), then for extremely clumped canopies such as coniferous forests (0.5 < Ω < 0.7) [Chen et al., 1997], LAIsh should contribute significantly to total canopy productivity. Furthermore, since Ω influences the ratio between sunlit and shaded leaves (as in the two-leaf case) or changes in PAR-intercepted area (as in the big-leaf case), it should have a considerable effect on canopy-level GPP [Baldocchi and Harley, 1995; Chen et al., 2003, 2012]. Typical values of Ω are 0.5–0.7 for conifer forests, 0.7–0.9 for broadleaf forests, and 0.9–1.0 for grass and crops [Chen, 1996; Chen et al., 1997].
After evaluations of two-leaf and big-leaf models against tower flux measurements, the effect of foliage clumping on GPP estimation was systematically investigated through a sensitivity analysis with the value of clumping index as an input in equation (2a) varying in a large range from 0.3 (very clumped) to 1 (randomly distributed foliage elements). This sensitivity analysis allows us to demonstrate the contribution of shaded leaves to canopy-level GPP and the sensitivity of this contribution to clumping. Both points can then be used to support or refute the necessity of sunlit-shaded leaf separation for modeling canopy photosynthesis.
2.6. Model Parameterization and Forcing
Since our main objective is to compare performances of two strategies of leaf-to-canopy upscaling using regional to global ecosystem models, where site-specific tuning is not preferred, leaf photosynthetic parameters such as maximum carboxylation rate (Vc,max), electron transport rate (Jmax) (equations (A2a) and (A2b), respectively), residual conductance (g0), and the slope of A to g relationship (in meters) were kept the same for both two-leaf and big-leaf models. Thus, the differences between the results can be solely explained by the mathematical formulation of these models. Our approach is justified because adjustment or aggregation of leaf parameters through the canopy, as has been proposed [e.g., Rastetter et al., 1992], is physiologically unrealistic for productivity modeling with big-leaf models (as will be shown further in this paper) and will turn big-leaf into a two-leaf or multilayered model (since it is impossible to obtain canopy-level parameters without an accurate canopy-level model), defeating the very purpose of big-leaf modeling.
Values in parentheses indicate adopted value ± STD.
15–100 (57 ± 7)
5–11 (6 ± 1.5)
0.011–0.0175 (0.01 ± 0.004)
15–130 (62.5 ± 17)
5–11 (8 ± 3)
0.011–0.00175 (0.013 ± 0.004)
25–90 (58 ± 20)
5–8 (6 ± 1.5)
0.011–0.00175 (0.013 ± 0.003)
Because BEPS, as well as other land-surface models, aims at regional applications with remote sensing inputs, our analysis used biochemical parameters derived for different plant functional types (PFTs) distributed among distinct climate zones. Thus, as mentioned by Groenendijk et al. , running it globally requires the parameters to be provided for every model grid cell, which is typically done by setting unique value for each PFT. For this reason we adopted leaf-level values for different PFTs from Kattge et al. , who conducted metadata analysis with 723 data points (Table 2, values in parentheses). However, accounting for the fact that the values of these parameters could be different at a latitudinal perspective, they have been adjusted with respect to climatic region (i.e., latitude). The reported value of standard deviation (Table 2) provides us with such flexibility. Nonetheless, one should bear in mind that latitude-based parameterization does not look very practical from a remote sensing point of view since the boundary of climate regions could not be easily defined.
BEPS was initialized to run for different land covers or a mixture of land covers, including broadleaf forest, coniferous forest, shrublands, C4 plants, and others (mostly crops and grass) aggregated from the detailed 1 km GLC2000 (http://www.eogeo.org/GLC2000) land-cover map, which was derived from SPOT4 VEGETATION imagery.
Daily LAI values at each site were extracted from the global LAI product [Deng et al., 2006], which is based on a 10-day synthesis of SPOT4 VEGETATION images (1 km spatial resolution). The LAI algorithm was developed based on the four-scale geometrical optical model and accounts for the variations of the reflectance in the various bands with the angles of the Sun and the satellite [Chen and Leblanc, 1997]. The resulted values are corrected for the clumping based on the global clumping index map produced from the multiangle observations of POLDER 1, 2, and 3 sensors [Chen et al., 2005].
Relevant meteorological inputs to the model included incoming radiation (W m−2), air temperature (°C), specific humidity (g kg−1), precipitation (mm), and a wind speed (m s−1) at 1/2 h resolution. Soil texture for each location was determined based on the fractions of clay, silt, and sand in soil and was used to calculate water holding capacity and soil water scaling parameter [Ju et al., 2006].
For the evaluation of these models, we relied on the canopy-scale measurements of the CO2 flux made using the eddy correlation technique [Baldocchi, 2003]. Site-level meteorological and soil data are also available from Ameriflux and Fluxnet Canada databases. Meteorological data were gap filled following a standard protocol as part of the North American Carbon Program (NACP) synthesis activity. Missing values (i.e., gaps) in the meteorological data records were filled using data of the nearest available climate station in the National Climatic Data Center's Global Surface Summary of the Day database or using DAYMET [Thornton et al., 1997].
3. Results and Discussion
3.1. Magnitude of GPP and Comparisons With Measured Results
Large differences were apparent between two-leaf and big-leaf model estimates of GPP for all sites examined (Figure 1). Since the behavior of both types of simulations is very consistent from year to year, for clarity only one representative year is displayed for each site.
Consistent with our hypothesis, the big-leaf model underestimated measured GPP for all structurally complex ecosystems, as evidenced by slopes < 1. Surprisingly, this underestimation occurred even in shrubland or low-LAI sites. In contrast, the two-leaf model had a slope closer to 1 at all sites, indicating greater fidelity between simulated and tower-derived GPP estimates. With respect to our second hypothesis, the results show that a greater percentage of variability in daily GPP was simulated by the two-leaf than the big-leaf model, especially at structurally complex coniferous sites. These points are primarily supported by the differences in the slope of the relationships between measured and modeled results, i.e., closer to 1 for the two-leaf model (ranging between 0.76 and 0.98, with an average of 0.86 ± 0.07) and very low for the big-leaf model (ranging from 0.4 to 0.52, with an average of 0.46 ± 0.04) as well as by coefficient of variation (CV) that equal 1.12, 0.68, and 0.51 for broadleaf, 0.65, 0.85, and 0.57 for conifers, and 1.21, 1.27, and 1.24 for shrublands for measured, two-leaf, and big-leaf models, respectively.
The close similarity between CV for two-leaf and big-leaf for shrubland sites could be explained by the naturally uniform distribution of canopy elements at the wetland site (classified as shrubland). These results support our hypothesis that GPP by structurally complex canopies cannot be adequately simulated by the big-leaf model.
3.2. Physiological Mechanisms of Big-Leaf GPP Underestimation
In contrast to evapotranspiration modeling, for which big-leaf approximation has been considered to be adequate [e.g., Raupach and Finnigan, 1988], the underestimation of GPP by the big-leaf model (when given the same leaf parameters as those in the two-leaf model) may be caused in part by simplified assumptions concerning the stomatal regulation of CO2 exchange as implied in the big-leaf formulation. Since significant resistance to carbon diffusion comes from leaf internal tissues [Chen et al., 1999; Warren, 2008], the big-leaf formulation essentially interrupts the pathway of CO2 flow from the outer air (stomatal cavity) to chloroplasts. By scaling only the stomatal conductance to the canopy level, the big-leaf approach artificially accumulates a large amount of stomata on one theoretical leaf (i.e., stomatal resistances of individual leaves are in parallel to the canopy resistance) while maintaining one leaf internal resistance to the gas flow. In this way, the total resistance to the CO2 flow is amplified as compared to the realistic case when leaves are all operating in parallel. When multiple layers of leaves work simultaneously, multiple internal resistances would operate in parallel, allowing CO2 flow to meet less resistance on its pathway from stomatal cavity to photosynthetic site.
Consequently, as was suggested by Chen et al.  and presented by Mercado et al. , big-leaf performance will be significantly improved by adjusting the vertical distribution of the parameters responsible for the internal control (i.e., Vm, Jmax, or compensation point). This last point actually signifies that the underestimation of GPP by the big-leaf model is by itself not ultimate proof of the fundamental failure of the big-leaf upscaling strategy, because at local scales, big-leaf underestimation could simply be remedied by parameterization of key model parameters to match observations. Our findings, however, show that consistently low GPP estimates by the big-leaf model for a range of ecosystems pose challenges for regional and global simulations in which these site-specific parameter adjustments are not practical. In this case, the adjusted big-leaf parameters could be (and were in our case) nearly twice as large as published values for a broad array of ecosystem types (Table 2). This outcome is similar to those reported by Mercado et al. , who showed increments of more than 60% in order to force big-leaf to match tower measurements.
3.3. Variability of Daily GPP
Even if big-leaf estimates could be boosted by inflating the leaf-level parameters to match observed GPP magnitudes, we have shown that daily and seasonal variability in GPP is more accurately captured by a two-leaf model, further demonstrating the shortcomings of the big-leaf mathematical formulation for GPP modeling. Figure 2 shows day-to-day variations of GPP obtained by the eddy covariance system versus the big-leaf and two-leaf model results, clearly indicating a greater dissimilarity in the amplitude of oscillation on both day-to-day and annual scales for the big-leaf model. Statistically, that dissimilarity was evaluated by comparing two standard measures of dispersion usually used for quantitative expression of the degree of variation in population: variance and interquartile range (IQR).
Both measures of variability are much smaller for big-leaf as compared with two-leaf and EC cases (Table 3). Averages values for EC, two-leaf, and big-leaf are 5.8 ± 3.7, 5.2 ± 3, and 1.9 ± 0.9, respectively, for variance, and 7.4 ± 5.3, 6.6 ± 4.0, and 2.6 ± 1.3, respectively, for IQR. Differences in the variances of daily GPP among modeled and measured estimates can be explained by the assumption in the big-leaf model that the entire canopy is a single unshaded leaf located at the canopy top. This approach diminishes the radiation control of, and consequently variation in, CO2 fixation because even if the radiation is mostly diffuse, irradiance levels often approach light-saturating conditions for a single horizontal leaf and the photosynthesis rate of the big-leaf is mostly determined by the maximum carboxylation rate, which depends on leaf temperature and nutrient status. This representation leads to the inability of the big-leaf approach to differentiate between clear and overcast days, resulting in unrealistic loss of model sensitivity to radiation load, and attenuates day-to-day amplitude in modeled GPP. The same lack of sensitivity explains the generally flat seasonal variation (Figure 2). In contract, the two-leaf model is sensitive to radiation variation because shaded leaves are often limited by the electron transport rate determined by the incident radiation level rather than by the maximum carboxylation rate. Under low-radiation conditions, canopy-level photosynthesis simulated by the two-leaf model is therefore strongly sensitive to small changes in incident radiation.
Table 3. Measures of Dispersion for Day-to-Day Variations of GPP Obtained by the Eddy Covariance, EC, Measurements and Simulated by Two-Leaf and Big-Leaf Modelsa
Letters in parentheses indicate deciduous broadleaf forests (DBFs), evergreen needle-leaf forests (ENFs), woody savanna (WSA), wetland (WET), or tundra (TUN) sites; AVG, average; STD, standard deviation. Fitted value stands for the case in which photosynthetic parameters have been arbitrarily increased in the big-leaf simulations to match the values measured by EC.
, where xi is a measured value, X is an average for the growing season, and n is the number of observations.
Interquartile Range = CDF−1 (0.75) − CDF−1 (0.25), where CDF is a cumulative distribution function.
Oas: 54° (DBF)
Syv: 46° (DBF)
UMB: 46° (DBF)
MOz: 39° (DBF)
Ton: 38° (WSA)
Obs: 54° (ENF)
Ho1: 45° (ENF)
NR1: 40° (ENF)
Mer: 45° (WET)
Ivo: 68° (TUN)
Average (±STD) for DBF
8.04 ± 3.1
7.04 ± 2.96
2.37 ± 0.68
3.72 ± 0.79
10.36 ± 4.72
8.79 ± 4.5
3.19 ± 1.14
Average (±STD) for ENF
3.94 ± 1.01
3.79 ± 0.25
1.82 ± 0.41
3.25 ± 1.3
4.79 ± 1.8
5.5 ± 0.19
2.62 ± 0.81
Average (±STD) for SHR
1.85 ± 0.72
1.53 ± 0.88
0.66 ± 0.57
1.89 ± 0.19
2.28 ± 1.54
1.8 ± 1.61
0.8 ± 0.85
Although the adjustment of the input parameters can improve the ability of a big-leaf model to reproduce the seasonal trend of simulated GPP as presented in Figure 3 for two selected sites, the lack of variance reproduced is still pronounced on a day-to-day scale compared with the two-leaf model results, as the variance of the simulated distribution remains below the observed case. Mercado et al.  obtained similar results regarding the dispersion of simulated data for an Amazonian forest, showing simulated GPP tightly distributed around an average and failing to capture the variability measured by an eddy covariance system. This lack of day-to-day variability in GPP simulated by the big-leaf model is caused not only by its inability to reflect the radiation control on shaded leaf photosynthesis as analyzed above but also by the amplified leaf internal resistance to the CO2 flow. The big-leaf formulation reduces only the stomatal resistance for multiple layers of leaves while the leaf internal resistance is unchanged no matter how many layers of leaves are operating simultaneously (i.e., internal resistances are in parallel in reality). This amplified internal resistance in the big-leaf formulation makes the model insensitive to driving factors affecting the canopy photosynthesis.
3.4. Impact of Canopy Clumping on Photosynthesis Upscaling
Our results indicate that discrepancy between the EC-measured and big-leaf modeled results is larger for coniferous than deciduous and shrubland sites because canopy structural features constrain GPP. This large discrepancy among land-cover types demonstrates the importance of the shaded part of a canopy for general evaluation of GPP, especially in clumped canopies, which are common for coniferous forests. Consequently, it is likely that the basis of the disagreement of measured (and two-leaf) versus big-leaf derived estimates of GPP is related to canopy structure and that this disagreement will exacerbate with increased clumping (i.e., a decrease in clumping index), as is the case for conifer sites. This suggestion is supported by the relative error (RE) between measured and big-leaf-simulated GPP estimates: ( were ∼29% higher for coniferous (61%) than for broadleaf (32%) and shrubland (47%) stands). In contrast, the difference between measured and two-leaf modeled GPPs for these land-cover types was only ∼4%.
The direct effect of changes in canopy architecture on simulated productivity for all sites is shown in Figure 4 by portraying the relative difference between two-leaf and big-leaf GPPs against the clumping index, which demonstrates that discrepancies between two-leaf and big-leaf estimates of GPP grew as clumping increases (decreasing clumping index). This trend can be explained by the contribution of the shaded part of the canopy to the total GPP because, theoretically, any decrease in Ω implies a decrease of LAIsun and a consequent increase of LAIsh. Even though a shaded leaf receives much less radiation than a sunlit one and its total quantum yield and stomatal conductance typically do not exceed those of a sunlit leaf [Šprtová and Marek, 1999], shaded leaves generally display greater light sensitivity at lower irradiances (i.e., higher light-use efficiency) and thus may constitute a large fraction of total canopy photosynthesis under conductions of high diffuse light [Alton, 2008; Gu et al., 2002]. The contribution of LAIsh to the total canopy photosynthesis can be as high as 40%–60% [Mercado et al., 2006].
Since a big-leaf model does not partition the canopy, an increase in clumping merely leads to a decrease in overall LAI (LAItot) and a resulting decrease in total simulated GPP. Consequently, the difference between two-leaf and big-leaf simulated GPPs rises to its highest for most clumped canopies. In the case of low clumping, the contribution of LAIsh will be much lower than that of LAIsun, and the differences between two-leaf and big-leaf estimates of GPP become smaller. However, even for Ω close to unity, big-leaf simulated GPP was only ∼50% of that obtained by two-leaf approach, suggesting that the contribution of LAIsh should not be ignored in any case.
Also apparent are differences in the ratio of big-leaf to two-leaf GPPs between the boreal (or cold) forest sites (CA-Oas, CA-Obs, and U.S.-NR1) and the sites located at lower latitudes. These differences are pronounced regardless of Ω and could be explained by the fact that even though plants enhance their light-use efficiency under low irradiance, this increase cannot compensate for the general decrease in canopy productivity under predominantly low-radiation loads in high-latitude cold environments. LAIsh in such environments is much less active than in warmer climates, and its contribution to a total photosynthesis is ∼10% lower, even for extremely clumped cases. In warmer environments the contribution of LAIsh remains stable over the entire range of clumping. In colder climates, its behavior was more similar to that of a deciduous forest.
An outlier in our results is the semiarid savanna site (U.S.-Ton), for which both models do not perform well in simulating its GPP. We suggest that the reason for such a similarity lies in low water availability and low light-use efficiency under predominantly high direct radiation loads, causing low stomatal conductance, which is not well captured by both models. This point, however, requires further investigation to properly scale between photosynthesis and stomatal conductance using the Ball-Woodrow-Berry equation.
3.5. Canopy Architecture and Global Scale GPP Modeling
Our finding that foliage clumping affects the outcome of carbon exchange simulations for a broad array of ecosystems when the canopy is treated as a big leaf indicates that poor representation of canopy architecture in models could have a dramatic impact on global estimates of GPP. This point is especially critical when using global LAI maps derived from optical remote sensing observations that usually relate more closely to the effective LAI rather than the true LAI [Chen et al., 2002]. Because LAI maps provide a basic input for many ecosystem models, incorrect representation of the ratio of sunlit-to-shaded leaf fractions in a canopy imbedded in effective LAI could lead to significant errors in modeled GPP on the global scale.
Chen et al.  investigated the impact of foliage clumping on the global GPP estimation by modeling productivity for different treatments of the canopy architecture using the effective and true LAI values. Their results indicate that for accurate global terrestrial GPP estimation, vegetation structure needs to be carefully described, at least in terms of precise representation of the ratio between shaded and sunlit parts. Inaccuracies in such a representation lead to either overestimation by about 8% (∼11 ± 1.6 picograms of carbon (pgC)) when the true LAI is used without considering clumping (sunlit LAI is overestimated and shaded LAI is underestimated) or underestimation by 15% (∼20.5 ± 3 pgC) when the effective LAI is used without considering clumping (sunlit LAI is accurate but shaded LAI is underestimated). Their study found that shaded leaves contribute 56%, 40%, and 39% to the total GPP for broadleaf evergreen forest, evergreen conifer forest, and shrub vegetation, respectively, with a global average of this ratio of 39%. Such a pronounced contribution cannot be ignored and has to be taken into account while upscaling from leaf to canopy in modeling vegetation photosynthesis, regardless of the upscaling approaches used.
By comparing the two most common strategies of leaf-to-canopy upscaling of CO2 fixation in ecosystem models across three land-cover types of varying canopy structural complexity in North America, we demonstrated that the separation of the canopy into its shaded and sunlit parts substantially improves the accuracy of modeled gross primary productivity magnitude and daily variability. Our multisite intercomparison adds evidence that big-leaf photosynthesis models should be discouraged or significantly modified for use in regional ecosystem modeling of GPP and demonstrates that a two-leaf approach is superior to the big-leaf one. Underestimation of GPP together with lower sensitivity of GPP to irradiance under the big-leaf mathematical formulation may be explained by (1) unrealistic amplification of leaf internal control on CO2 pathway from stomatal cavity to photosynthetic machinery, and (2) inaccurate representation of variability in direct or diffuse radiation and its effect on CO2 fixation.
Our study demonstrates that separating a canopy into sunlit and shaded leaf components (i.e., the two-leaf approach) markedly outperforms the big-leaf approach in simulating GPP for a wide range of ecosystem types with different complexity of canopy architecture. Among the coniferous, deciduous, and shrubland ecosystems examined, the difference between big-leaf and two-leaf models was most pronounced for coniferous sites, which display the highest canopy clumping. Under a given sky condition, clumped canopies have more shaded leaves than those that are less clumped, and therefore GPP is more underestimated by the big-leaf model when considering structurally complex canopies because of its inability to consider the contribution of shaded leaves. Our foliage clumping sensitivity analysis showed that for extremely clumped canopies, the contribution of the shaded part to the total simulated GPP can be as high as 70% and never below ∼40%, even for randomly oriented leaves. These results indicate that accurate estimation of GPP for a broad array of canopy architectures requires quantitative understanding of the leaf area arrangement within the canopy and highlights the value of the two-leaf upscaling strategy.
A1. Canopy Photosynthesis
The rates of photosynthesis are calculated by combining Farquhar's model [Farquhar et al., 1980] with a model describing the flow of CO2 from inside the stomatal cavity to the free air [Leuning, 1997]:
where Ac and Aj are Rubisco-limited and light-limited gross photosynthesis rates, respectively (μmol m−2 s−1); Vm is the maximum carboxylation rate (μmol m−2 s−1); J is the electron transport rate (μmol m−2 s−1); Ci and Oi are the intercellular CO2 and oxygen concentrations, respectively (mol mol−1); Γ is the CO2 compensation point without dark respiration (mol mol−1); and K is the function of enzyme kinetics, calculated as K = Kc(1+O2)/Ko where Kc and Ko are Michaelis-Menten constants for CO2 and O2, respectively and could be found in the work of Chen et al. . The values of the biochemical parameters have been calculated based on the vertical profile of nitrogen content as explained in detail further in this appendix.
The net rate of CO2 assimilation (either sunlit or shaded parts) is then calculated as
with Rd = 0.015Vm representing a leaf dark respiration.
A2. Stomatal Conductance
The indirect influence of solar irradiance on stomatal conductance (g) becomes apparent in the Ball-Woodrow-Barry equation [Ball et al., 1987] that linearly relates g to the photosynthesis rate (A):
where m is a slope that is plant species dependent, Rh is the relative humidity at the leaf surface, P is the atmospheric pressure, Cs is the CO2 concentration at the leaf surface, and g0 is a residual conductance.
The influence of soil water content on stomatal conductance is evaluated by adding a soil moisture scaling factor to the Ball-Woodrow-Berry formulation as described in detail by Ju et al. . For simultaneous estimations of A (required for calculation of g; equation (A3)) and g (required for calculation of A; equation (A1)), BEPS uses an iteration procedure exploiting the analytical solution proposed by Baldocchi .
A3. Sunlit and Shaded Leaf Irradiance
Total solar radiation above the plant canopy is partitioned into diffuse (Idif) and direct (Idir) components, with the latter a reminder of a former (Idir = Ig− Idif) [Erbs et al., 1982], which was modified and validated by Black et al.  for midlatitudes:
where Ig is the global radiation (W m−2) and R = [Ig/(S0 cosθ)], with solar constant S0 = 1367 (W m−2).
The diffuse radiation fraction estimated from this equation is within the variation range of data assembled by Spitters  from nine locations around the globe, but is about 5%–10% lower than the mean value across the entire R range. It is important to mention, however, that this equation would underestimate the diffuse fraction for air masses with large aerosol contents.
The sunlit leaf irradiance (Isun) is then calculated as
where α ∼ 60° is mean leaf-Sun angle for a canopy with spherical leaf angle distribution. The first term on the right-hand side of equation (A5) represents the contribution of the direct beam, while the second term accounts for the diffused radiation (i.e., the mean shaded leaf irradiance), and it is developed based on radiative transfer physics [Chen et al., 1999]:
where the first term on the right-hand side quantifies the average diffuse irradiance on shaded leaves (which originates from both the sky irradiance and multiple scattering of the incoming radiation within the canopy) by distributing the total intercepted diffuse radiation from the sky to the total LAI involved; is the diffuse radiation below the plant canopy; is a representative zenith angle for diffuse radiation transmission; and C = 0.07ΩIdir(1.1 − 0.1 LAI)exp(−cosθ) is added to include the enhancement of diffuse radiation that is due to multiple scattering of the incoming direct radiation.
A4. Nitrogen-Weighted Vm and Jm for Sunlit and Shaded Leaves
As leaf nitrogen content per unit leaf area N (LAI) decreases exponentially from the top to the bottom of a canopy, it can be expressed as
where N0 is the nitrogen content at the top of the canopy and kn is the leaf nitrogen content decay rate with increasing depth into the canopy, taken as equal to 0.3, after de Pury and Farquhar .
The leaf maximum Rubisco capacity (Vm) is linearly related to leaf nitrogen content (Nl) [Field, 1983], that is, Vm = χnNl, in which χn is the ratio of measured Rubisco capacity to leaf nitrogen [de Pury and Farquhar, 1997; Dai et al., 2004]. Therefore, the vertical profile of leaf nitrogen is modeled as a function of LAI and hence Vm is given by
where Vm,0 is Vm at the top of the canopy (LAI = 0) at 25°C. The values at the top of the canopy (i.e., Vm,0 and N0) are taken as their mean values plus one standard deviation. See Table 2 for PFT-dependent values of χn.
Because the fractions of sunlit (fsun = e-kLAI) and shaded (fsh = 1-e-kLAI) leaf areas also vary with the depth into the canopy, the mean values of eaf nitrogen content for sunlit and shaded leaves and their corresponding Vm values can be obtained through vertical integrations with respect to LAI [Chen et al., 2012]:
where k = G(θ)Ω/cosθ; G(θ) is the projection coefficient, usually taken as 0.5 for spherical leaf angle distribution, Ω is the clumping index, and θ is the solar zenith angle.
As a result, the maximum electronic transport rates for the representative sunlit and shaded leaves are obtained as
In this way, the effects of the vertical nitrogen gradient in the canopy on both the maximum carboxylation rate and the maximum electron transport rate are considered.
This study was conducted under the auspices of the North American Carbon Program site-model intercomparison synthesis. This research was supported by the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) (GR464) and the Canadian Carbon Program (CCP), also funded by CFCAS. U.S.-Syv was funded by the Office of Science (BER), U.S. Department of Energy Terrestrial Carbon Processes program, grant DE-FG02-00ER63023. We acknowledge the agencies that supported the flux tower operations of the towers used here, which are all part of CCP and Ameriflux. We specifically acknowledge the principal investigators of each studied site and in particular Dennis Baldocchi, Alan Barr, Peter Curtis, Lianhong Gu, Tilden Meyers, David Hollinger, Russ Monson, Walter Oechel, Nigel Roulet, and Elyn Humphreys. M.S. is very thankful to A. Kreimer for immeasurable help in data processing and programming.